Honors Advanced AlgebraName:______

Apps of Right Triangles – Bearing ProblemsDate:______

Assignment #3Period:______

1.A plane flies 1.3 hr at 110 mph on a bearing of 40°. It then turns and flies 1.5 hr at the same speed on a bearing of 130°. How far is the plane from its starting point?

2.A ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km. Find the distance traveled from the starting point to the ending point.

3.Two ships leave a port at the same time. The first ship sails on a bearing of 40° at 18 knots (nautical miles per hour) and the second at a bearing of 130° at 26 knots. How far apart are they after 1.5 hours.?

4.Two lighthouses are located on a north-south line. From lighthouse A the bearing of a ship 3742 m away is 129.72°. From lighthouse B the bearing of the ship is 39.72°. Find the distance between the lighthouses.

5.A ship leaves its home port and sails on a bearing of N 28.17° E. Another ship leaves the same port at the same time and sails on a bearing of S 61.83° E. If the first ship sails at 24.0 mph and the second sails at 28.0 mph, find the distance between the two ships after 4 hr.

6.Radio direction finders are set up at points A and B, which are 2.50 mi apart on an east-west line. From A it is found that the bearing of the signal from a radio transmitter is N 36.33° E, while from B the bearing of the same signal is N 53.67° W. Find the distance of the transmitter from B.

7.The bearing from Winston-Salem, North Carolina, to Danville, Virginia, is N 42° E. The bearing from Danville to Goldsboro, North Carolina, is S 48° E. A car driven by Mark Ferrari, traveling at 60 mph, takes 1 hr to go from Winston-Salem to Danville and 1.8 hr to go from Danville to Goldsboro. Find the distance from Winston-Salem to Goldsboro.

8.The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 60 mph needs 1.25 hr to go from Atlanta to Macon and 1.75 hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

9.Find the minimum height h above the surface of the Earth so that a pilot at point A in the figure can see an object on the horizon at C, 125 mi away. Assume that the radius of the Earth is 4.00 X 103 mi.

10.In one area, the lowest angle of elevation of the sun in winter is 23.33°. Find the minimum distance x that a plant needing full sun can be placed from a fence 4.65 ft high.

11.A tunnel is to be dug from A to B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B.

12.A piece of land has the shape shown in the figure. Find x.

Solutions:1) 218.3 mi2) 148.7 mi3) 47.4 mi4) 5855.7 mi 5) 147.5 m6) 2.0 mi

7) 123.5 mi8) 129.0 mi9) 2.0 mi10) 10.8 ft11) 36.0°12) 84.7 m